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The Wigner transform is the bridge between Hilbert space operators to phase-space quantities (c-numbers). Use for issues relating to the Weyl correspondence (the inverse of the Wigner transform), the Wigner function (the Wigner-transform of the density matrix) and, in general, Quantum Mechanics in phase space issues, such as the *-product, the Wigner transform of the operator multiplication operation. May also use for distributions such as the Husimi.

4 votes

Bounding derivatives of the Wigner function using phase-space tails

Felipe Hernández and I ended up showing that the answer is yes for both pure and mixed states: "Rapidly Decaying Wigner Functions are Schwartz Functions" [arXiv:2103.14183]. We were able to laboriousl …
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5 votes

An example of a quantum system for which Wigner function transitions to negative values

The times that the Wigner function is positive does not mean it should be interpreted as a probability distribution. (What events would it be the probability distribution of? Certainly not a fuzzy j …
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